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US7786991B2 - Applications of interval arithmetic for …
https://patents.google.com/patent/US7786991B2/en
Ray tracing is based on massively parallel geometrical queries, executed against some spatially ordered geometrical database. The interval traversal algorithm may …
Ray tracing general parametric surfaces using …
https://www.cs.drexel.edu/~david/Classes/Papers/Barth_1994.pdf
Ray tracing general parametric surfaces using interval arithmetic. Wilhelm Barth 1, Roland Lieger, and Michael Schindler. Technical University Vienna, Department of Computer Graphics, Karlsplatz 13/186, A-1040 Vienna, Austria. 1e-mail: barth @eichow.t uwien.ac.at. This paper describes an algorithm for ray tracing general parametric surfaces. After dividing the surface adaptively into …
Ray tracing general parametric surfaces using interval …
https://link.springer.com/article/10.1007/BF01900662
This paper describes an algorithm for ray tracing general parametric surfaces. After dividing the surface adaptively into small parts, a binary tree of these parts is built. For each part a bounding volume is calculated with interval arithmetic.
Fast Ray Tracing of Arbitrary Implicit Surfaces with …
https://www.sci.utah.edu/~knolla/cgrtia.pdf
3.1. Ray Tracing Implicit Surfaces A surface S in implicit form in 3D is the set of solutions of an equation f(x,y,z)=0 (1) where f :Ω⊆R3 →R. In ray tracing, we seek the intersec-tion of a ray ~p(t)=~o+td~ (2) with this surface S. By simple substitution of these position coordinates, we derive a unidimensional expression ft(t)= f(ox +tdx,oy +tdy,oz +tdz) (3)
Improvements in the Ray Tracing of Implicit Surfaces …
http://gilab.udg.edu/wp-content/uploads/thesis/JorgeFlorezPhD.pdf
there are still two open problems in the ray tracing of implicit surfaces based on Interval Arithmetic: • Ray tracing is slow, and Interval Arithmetic is slow too. Many floating-point operations are required for every Interval Arithmetic operation (besides rounding). For that reason, the ray tracing becomes even slower.
Fast Ray Tracing of Arbitrary Implicit Surfaces with …
https://www.sci.utah.edu/publications/knoll09/CGF-implicits-2009.pdf
Ray tracing implicit surfaces A surfaceSin implicit form in 3D is the set of solutions of an equation f(x,y,z) = 0(1) wheref:3⊆R →R.Inraytracing,weseektheintersec- tion of a ray p(t) =o+td(2) with this surfaceS. By simple substitution of these position coordinates, we derive a …
Interactive Ray Tracing of Arbitrary Implicits with …
https://www.sci.utah.edu/publications/knoll07/rtia-rt07.pdf
interval arithmetic library with a novel coherent ray tracing algo-rithm for implicits that performs coherent spatial bisection without the need for an explicit acceleration structure. We require no spe-cial hardware, other than SIMD vector instructions prevalent on all modern CPUs. To render, we require only the implicit function
CSG Operations of Arbitrary Primitives with Interval …
https://www.sci.utah.edu/publications/SCITechReports/UUSCI-2008-008.pdf
In ray tracing, we seek the intersection of a ray p(t)=o+td (2) with this surface S. By simple substitution of these position coordinates, we derive a unidimensional expression f t(t)= f(o x+td x,o y+td y,o z+td z) (3) and solve where f t(t) = 0 for the smallest t > 0.
Reliable Ray Tracing by Linear Interval Estimations
https://interval.louisiana.edu/preprints/doc64.pdf
Reliable Ray Tracing by Linear Interval Estimations Abstract Recently Buhler˜ has introduced a new type of bounding volume for parametric surfaces. These bounding volumes, which Buhler˜ calls Linear Interval Estimations (LIEs), are parametrized with the same parametrization as the surfaces they bound. We report on the application of LIEs to the ray
Reliable algorithms for ray intersection in ... - New …
https://cs.nyu.edu/exact/pap/mesh/raytracing-robust.pdf
interval arithmetic for ray tracing implicit surfaces. W e an-alyze when and how to use interval arithmetic as an alter - native to the methods used in PO V -Ray for ray inter section. Interval methods ar e applied as robust appr oac hes for solv-ing the ray-surface inter section pr oblem; i.e. to Þnd the minimal root in a set of analytic functions.
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